﻿68 Dr. Norman Campbell on the 



probably the view that Venn would have held if he had ever 

 considered the nature of: physical measurement. But the 

 further view often attributed to Venn, though it is doubtful 

 whether he actually held it, that probability is always 

 measurable in terms of chance — this view will not be upheld, 

 but, so far as it is discussed at all, will be combated. 



Many of the ideas and terms used in the discussion are 

 explained more fully in my ' Physics,' to which references are 

 made by the letter P. In fact, this paper may be regarded as a 

 substitute for pp. 168-183 of that book, some of the difficulties 

 of which are avoided by the alternative method of treatment. 

 However, I should like to add that I do not accept any of 

 the criticisms that have been directed against those pages by 

 others. 



2. Suppose we are presented with a pair of dice, and asked 

 what is the chance that when one of them is thrown it will 

 turn up six. The answer may be different for the two dice. 

 If one of them is accurately cubical with its centre of mass 

 accural ely at the centre of the cube, while the other has 

 corners and edges variously rounded and is loaded so that 

 the centre of mass is appreciably nearer one face than 

 another, then the answer will be different. On the other 

 hand, if in all respects the dice are the same, then the 

 answer will be the same ; even if they are both inaccurate 

 in form and both loaded — the inaccuracy of form and the 

 loading being the same — the chance that they will turn up 

 six will be the same. This chance is something uniformly 

 associated with and changing with the structure of the die, 

 just as is (say) the electrical resistance. This uniform 

 association of the resistance with the other characteristics 

 of the die is what we assert when we say that; the resis- 

 tance is a physical property of the die, and accordingly 

 the chance of turning up six is a physical property as much 

 as the resistance. 



Moreover, the chance is measured by essentially the same 

 process as that by which the resistance is measured. Resist- 

 ance is measured (in its original meaning) as a derived 

 magnitude by means of a numerical law (P. Ch. xiii.).. We 

 place two electrodes in contact with opposite faces of the 

 die, and measure the current which flows through it when 

 measured potential differences are maintained between the 

 electrodes. We then plot current against P.D., and find we 

 can draw a straight line through (or more accurately 

 among) the resulting points. The fact that the graph is a 



